$L^p$ weighted inequalities for the dyadic square function

Uchiyama, Akihito

L^{p}

weighted inequalities for the dyadic square function

Uchiyama, Akihito

Studia Mathematica, Tome 113 (1995), p. 135-149 / Harvested from The Polish Digital Mathematics Library

Access to full text
Full (PDF)

Résumé

We prove that $ʃ {(S_{d} f)}^{p} V d x \leq C_{p, n} ʃ {| f |}^{p} M_{d}^{([p / 2] + 2)} V d x$ , where $S_{d}$ is the dyadic square function, $M_{d}^{(k)}$ is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.

Publié le : 1995-01-01

Zbl 0842.42010

EUDML-ID : urn:eudml:doc:216204

@article{bwmeta1.element.bwnjournal-article-smv115i2p135bwm,
     author = {Akihito Uchiyama},
     title = {$L^p$ weighted inequalities for the dyadic square function},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {135-149},
     zbl = {0842.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv115i2p135bwm}
}

Uchiyama, Akihito. $L^p$ weighted inequalities for the dyadic square function. Studia Mathematica, Tome 113 (1995) pp. 135-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv115i2p135bwm/

Bibliographie

[00000] [CWW] S. Y. A. Chang, J. M. Wilson and T. H. Wolff, Some weighted norm inequalities concerning the Schrödinger operators, Comment. Math. Helv. 60 (1985), 217-246. | Zbl 0575.42025

[00001] [CW] S. Chanillo and R. L. Wheeden, Some weighted norm inequalities for the area integral, Indiana Univ. Math. J. 36 (1987), 277-294. | Zbl 0598.34019

[00002] [C] R. R. Coifman, A real-variable characterization of $H^{p}$ , Studia Math. 51 (1974), 269-274. | Zbl 0289.46037

[00003] [D] W. R. Derrick, Open problems in singular integral theory, J. Integral Equations Appl. 5 (1993), 23-28. | Zbl 0773.42011

[00004] [Gn] J. B. Garnett, Bounded Analytic Functions, Pure and Appl. Math. 96, Academic Press, 1981.

[00005] [Gs] A. M. Garsia, Martingale Inequalities, Seminar Notes on Recent Progress, Benjamin, 1973.

[00006] [P] C. Pérez, Weighted norm inequalities for singular integral operators, J. London Math. Soc. (2) 49 (1994), 296-308. | Zbl 0797.42010

[00007] [S1] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.

[00008] [S2] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993.

[00009] [W1] J. M. Wilson, Weighted inequalities for the dyadic square functions without dyadic $A_{\infty}$ , Duke Math. J. 55 (1987), 19-49.

[00010] [W2] J. M. Wilson, A sharp inequality for the square function, ibid., 879-887. | Zbl 0639.42017

[00011] [W3] J. M. Wilson, $L^{p}$ weighted norm inequalities for the square function 0< p< 2, Illinois J. Math. 33 (1989), 361-366.

[00012] [W4] J. M. Wilson, Weighted inequalities for the square function, in: Contemp. Math. 91, Amer. Math. Soc., 1989, 299-305.

[00013] [W5] J. M. Wilson, Weighted norm inequalities for the continuous square function, Trans. Amer. Math. Soc. 314 (1989), 661-692. | Zbl 0689.42016

[00014] [W6] J. M. Wilson, Chanillo-Wheeden inequalities for 0< p≤ 1, J. London Math. Soc. (2) 41 (1990), 283-294. | Zbl 0712.42032

[00015] [W7] J. M. Wilson, Some two-parameter square function inequalities, Indiana Univ. Math. J. 40 (1991), 419-442. | Zbl 0734.42007